Many cases of 'asthma' and 'migraine' are misdiagnosed by overworked, careless GP's. Unfortunately these are put on permanent medical record.
My advice is to get a second opinion, in writing, by a leading expert in that field and make sure that these are kept with your medical files. I know from personal experience that this will work in your favour, if you have been given a wrong diagnosis. It will cost you a fair bit of money, but it is well worth it if you want a flying career.
BFB